Analytic torsion on manifolds with edges

作者：Mazzeo Rafe^*; Vertman Boris

来源：Advances in Mathematics, 2012, 231(2): 1000-1040.

DOI：10.1016/j.aim.2012.05.008

• Analytic torsion
• Cheeger-Muller theorem
• Incomplete edge singularity
• Heat trace asymptotics

Let (M, g) be an odd-dimensional incomplete compact Riemannian singular space with a simple edge singularity. We study the analytic torsion on M, and in particular consider how it depends on the metric g. If g is an admissible edge metric, we prove that the torsion zeta function is holomorphic near s = 0, hence the torsion is well-defined, but possibly depends on g. In general dimensions, we prove that the torsion depends only on the asymptotic structure of g near the singular stratum of M; when the dimension of the edge is odd, we prove that the analytic torsion is independent of the choice of even admissible edge metrics. The main tool is the construction, via the methodology of geometric microlocal analysis, of the heat kernel for the Friedrichs extension of the Hodge Laplacian in all degrees. In this way we obtain detailed asymptotics of this heat kernel and its trace. Published by Elsevier Inc.

• 出版日期2012-10-1